Viscosity parameter in dissipative accretion flows with mass outflow around black holes

Abstract

Numerical hydrodynamic simulation of inviscid and viscous flows have shown that significant outflows could be produced from the CENtrifugal pressure supported BOundary Layer or CENBOL of an advective disk. However, this barrier is weakened in presence of viscosity, more so, if there are explicit energy dissipations at the boundary layer itself. We study effects of viscosity and energy dissipation theoretically on the outflow rate and show that as the viscosity or energy dissipation (or both) rises, the prospect of formation of outflows is greatly reduced, thereby verifying results obtained through observations and numerical simulations. Indeed, we find that in a dissipative viscous flow, shocks in presence of outflows can be produced only if the Shakura-Sunyaev viscosity parameter {\alpha} is less than 0.2. This is a direct consequence of modification of the Rankine-Hugoniot relation across the shock in a viscous flow, when the energy dissipation and mass loss in the form of outflows from the post-shock region are included. If we ignore the effects of mass loss altogether, the standing dissipative shocks in viscous flows may occur only if {\alpha} < 0.27. These limits are tighter than the absolute limit of {\alpha} = 0.3 valid for a situation when the shock itself neither dissipates energy nor any outflow is formed. We compute typical viscosity parameters required to understand spectral and temporal properties of several black hole candidates such as GX399-4, MAXI J1659-152 and MAXI J1836-194 and find that required {\alpha} are indeed well within our prescribed limit.